The use of pneumococcal conjugate vaccines (PCVs) in children has a strong indirect effect on disease rates in adults. When children are vaccinated with PCVs, other serotypes that are not targeted by the vaccine can increase in frequency (serotype replacement) and reduce the direct and indirect benefits of the vaccine. To understand and predict the likely impacts of serotype replacement, it is important to know how patterns in the transmission of serotypes among children relate to disease rates in adults. We used data on pneumococcal carriage and disease from Navajo Nation children and adults collected before and after the routine use of PCVs (1998-2012). Using regression models within a Bayesian framework, we found that serotype-specific carriage and invasiveness (disease incidence divided by carriage prevalence) had similar patterns in children and adults. Moreover, carriage in children, invasiveness in children, and a serotype-specific random intercept (which captured additional variation associated with the serotypes) could predict the incidence serotype-specific pneumococcal disease in adults 18-39 years of age and those 40 years of age or older in the era of routine use of PCVs. These models could help us predict the effects of future pneumococcal vaccine use in children on disease rates in adults, and the modeling approach developed here could be used to test these findings in other settings.